Name: ________________________________
Honor Code Acknowledgment: ___________________
Random Quiz # 11
CPS 100, Spring 1996
Due: March 1
Problem 1: Russian Tea Leaves (2 points)
True or False: In an AVL tree all the leaves are at the same level
(height)
Problem 1: Tight Rope (4 points)
The function IsHeightBalanced below
determines whether a tree is height-balanced (for all nodes, left and
right subtrees differ by no more than one).
<![CDATA[
bool IsHeightBalanced(TNode * tree)
// postcondition: returns true if tree is balanced, else returns false
{
if (tree != 0)
{
if (IsHeightBalanced(tree->left) &&
IsHeightBalanced(tree->right) &&
abs(Height(tree->left) - Height(tree->right)) <= 1)
{
return true;
}
return false;
}
return true;
}
]]>
The complexity of this function is greater than O(n). What is
the complexity and why?
Write an auxiliary function, so that the body of
IsHeightBalanced will be
<![CDATA[
// some variable definitions
return IsAuxBalanced(tree,hleft,hright);
]]>
and so that IsAuxBalanced works in O(n) time.